First I think coping is a form of resistance C- covering O-over P-painful E-emotions. How about instead of choose coping, choose discovery.

Maybe what we don't like in another is what we don't accept in ourselves. I think it is a form of that. Whatever someone is showing us may hit another button in ourselves. For instance, maybe someone is a 'know-it'all' and we react with boredom, judgment, missing out of discovery, etc. Whatever we choose to feel is the relationship that needs attention, not the person showing us. They now become our teachers of where we aren't accepting a part of us.

That's what I choose to focus on when someone shows me my resistance. Let the focus go from them onto that part of ourselves that need attention and love.

In all probability, there may be truth to the saw that what we dislike in another is some unresolved problem within ourself (ourselves). But, I do think there are times when we dislike someone who is self-referential.
We may have this characteristic, but maybe not.

I have been told that the things you dislike about another person, are the things of which you dislike about yourself - whether you are consciously aware of it, or not. When some other person reflects an action, or a reaction of which you distain,it is known as "mirroring."

I am not sure that I agree with that analogy, however, it does make me reflect upon myself, and my actions and reactions therein.

Let everyone use their gifts of giving. It is only when you receive the gift of helping that you are allowing them to use their gifts. Your gift will be at that time the gift of receiving!! It is a great exchange of engergies, the more you give, the more you can receive and vice versa. Have a nice day!